I think it's great you are mixing it up and the missions seem lore friendly but here are a few observations:

It would be nice to have some sort of briefing at the beginning why you are going back in there. As of now(and I realize it's a beta) there is just nothing. I was like is the level starting? It doesn't have to be a treatise but something like "Our tech-priests(Or Dion Warwick's psychic friends, whatever) have detected some vital data(information, whatever) initially missed during the initial mission. We are sending you back in to complete the tasks set out by mission specialist commander "Phil McKraken", or whatever(if you can't get the original actor use a dev or something to voice the missions)Follow his orders like they were my own. The emporer protects" or some other lore friendly briefing(only if you can't get the original actor). This can be used on all the special missions. If you wanted to be super good you could insert the name of the vessel, but it's probably easier to have a generic one or at least a place holder for now. That way when new orders come through there is at least some sort of notification on what is going on.

Possible bug but probably not:

On the Grimoire missions(book gathering) I wasn't able to find the book in the small library and I searched everywhere(happened twice). The only reason I say "possible" bug is on searching the room with the big bell I found the book there in two different locations. One near a dead tech-priest right next to the Bell, and once on the podium at the top of the stairs. So I'm thinking I may have just missed it but we literally looked in every corner and the pews where it normally was. I'll withhold calling it a bug until I can reproduce it. Maybe write up a little tutorial on each of the new "missions". Don't tell us where the books are, but say something like "The books will be randomly placed in the room where you need to find the grimoires. Search well brothers" or whatever.

Also just some quick observations. It seems the difficulty is a bit higher than normal which is good. It seems that "normal" is now "hard" etc. Now if we can just fix the damn autocannon to tighten up the spread slightly that would be great. Good job Devs for mixing it up. This game is really coming along.

The randomized objectives and starting locations is a good improvement and kind of gives existing maps a whole new play through experience.

Did several play troughs and there were a few different mission types, Escort, Find and Retrieve, Data Collection and Flip a switch.
They appeared to re-appears at pre-set locations and they repeated and this became noticeable quickly, now I'm guessing only a few have been added to get some initial feedback, I really do hope a lot more location will be added, to maintain the "random" feel to it.

Additional things that should be consider to be added.
-Random broken doors, that might need to be destroyed

To add to the existing objective types,
-collapsing a tunnel/corridor or close/seal an access hatch or door
There are plenty of dead end corridors with xenos spawning points that could be blocked off.
-Search and Destroy,
find a Xenos boss kind of creator and exterminate it
-Deployed scanning equipment, 3 location to detect/find object/xenos/fallen brother

Between objectives, the boss guy contacts you to brief you on your next objective progression. This however really needs to be done in voice over, when there is this tense combat fight going on, I most certainly don't have time to focus and read what the boss guy is staying. This brings me to the next point, in case one didn't read (or hear in case of future voice over) what the boss guy had to say, sense of direction, next objective. We have HUD markers giving us some sense of direction, having one or a few lines of text pinned to our HUD describing our next objective, would add a lot more guidance.

ill just add my Impressions to this post.
First of all great work. This is exactly what i wished for since day 1. The variance of the missions and the situations you are forced in really add a great replay value on the maps. It rewards careful step by step planing and is hard enough to be challenging but not unfair since a squad wipe can be traced to ones own errors instead of gltches and bugs.
I have read in the post above that collapsed tunnels would also put up a variance and can be added after an objective is done.
I think this generally a good idea, if you put up a variance of the map at the start. Further into the game changing the map is a little hrash since a lot of the succes of the mission is done through slowly shutting out the genestealers. To collaps a passage after you already done an objective can ruin a whole run, since your previously planned route now is collapsed and you have to batter down previously locked doors to advance, which is really not what you want to do , especially on higher difficulty.
All in all this game started of rough but is becoming more and more the diamond it should be. As always give us more maps/weapons.

To collaps a passage after you already done an objective can ruin a whole run, since your previously planned route now is collapsed and you have to batter down previously locked doors to advance, which is really not what you want to do , especially on higher difficulty.

I don't fully agree with you, but do very well understand what you mean with the higher difficulty settings and being forced to knock down a previously locked down will makes things more challenging.

I've played through the game on No Mercy difficulty in coop and as a team we had to navigate our way to the next objective, not knowing what our objective would be after that, simply because we played it for the first time, we have been forced to knock down previously closed doors and lived to tell the tale, as well as died trying.

This created truly magnificent tense moments, were one is glad to make it to the next door that we could be blocked again to catch a brief breather.

Once you know your route and what comes next, you will end up taking a different route just so you can block doors to keep your rear guard save as your work your way through the known campaign objectives. Even though this a valid tactic that I will also use, with random objectives, you no longer know what the best route will be and you might end up having to go back through a door you previously blocked.

I'm very much looking forward to not knowing what comes next and facing that challenge head on...

i loved the Machanicum Priest Warping in, twas really surprising and cool to see that. Want more of that stuff!

Each of these Mission could have a Random Factor namely
1. Terminator Squad is Split apart when entering Level and has to Meet at a set Location2. Sealing doors so you can advance to next Missions( get overruned while try to seal set Doors)

Defend Construction SiteDefend the poor Adepts/ Priest while they Construct whatever...
1. defend for a set time

Find and deliver Relics to Adepts/ Priests

Assassination*Assassinate one or Multiple HVT`s not sure if this is already in...

Extermination
Get Overruned by Nids*Needs to be in a Location where there are multiple Doors, so you are forced to Tunnel them to one Corridor and unleash hell

Where there is uncertainty, I shall bring light
Where there is doubt, I shall sow faith
Where there is shame, I shall point atonement
Where there is rage, I shall show its course
My word in the soul shall be as my bolter in the field.

The update is great, just a shame they plan to finally kill the game. MIght as well take the servers down because of what they plan for in Q4.

Why kkill the Game? explain...

Where there is uncertainty, I shall bring light
Where there is doubt, I shall sow faith
Where there is shame, I shall point atonement
Where there is rage, I shall show its course
My word in the soul shall be as my bolter in the field.